The volume of a hemisphere is numerically equal to four times its cruved surface area. Find its radius.

Question

The volume of a hemisphere is numerically equal to four times its cruved surface area. Find its radius.

1. A. 12 cm (Correct answer)
2. B. 15 cm
3. C. 16 cm
4. D. 17 cm

Correct Answer

Option A — 12 cm

Detailed Solution & Explanation

The correct answer is 12 cm.

Key Points

• Volume of a hemisphere = (2/3)πr³; curved surface area = 2πr².
• Setting volume numerically equal to 4 × CSA:
• (2/3)πr³ = 4·2πr² → (2/3)r³ = 8r² → r = 8·(3/2) = 12 cm.
• The π and one power of r cancel, so 'volume = k × surface area' problems always reduce to a single linear equation in r.